Highest Common Factor of 1500, 9962 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 1500, 9962 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1500, 9962 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 1500, 9962 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 1500, 9962 is 2.
HCF(1500, 9962) = 2
HCF of 1500, 9962 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1500, 9962 is 2.
Highest Common Factor of 1500,9962 is 2
Step 1: Since 9962 > 1500, we apply the division lemma to 9962 and 1500, to get
9962 = 1500 x 6 + 962
Step 2: Since the reminder 1500 ≠ 0, we apply division lemma to 962 and 1500, to get
1500 = 962 x 1 + 538
Step 3: We consider the new divisor 962 and the new remainder 538, and apply the division lemma to get
962 = 538 x 1 + 424
We consider the new divisor 538 and the new remainder 424,and apply the division lemma to get
538 = 424 x 1 + 114
We consider the new divisor 424 and the new remainder 114,and apply the division lemma to get
424 = 114 x 3 + 82
We consider the new divisor 114 and the new remainder 82,and apply the division lemma to get
114 = 82 x 1 + 32
We consider the new divisor 82 and the new remainder 32,and apply the division lemma to get
82 = 32 x 2 + 18
We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get
32 = 18 x 1 + 14
We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1500 and 9962 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(82,32) = HCF(114,82) = HCF(424,114) = HCF(538,424) = HCF(962,538) = HCF(1500,962) = HCF(9962,1500) .
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Frequently Asked Questions on HCF of 1500, 9962 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 1500, 9962?
Answer: HCF of 1500, 9962 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1500, 9962 using Euclid's Algorithm?
Answer: For arbitrary numbers 1500, 9962 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.